2019/01/28 by Manuel Saorín, Alexander Zimmermann, Saorín, Manuel +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.CT #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1901.09713
arxiv created 2019/01/28 · arxiv updated 2019/01/29
In previous work, based on work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to degeneration of modules. In triangulated categories it is surprising that the zero object may degenerate. We study this systematically. In particular we show that the degeneration of the zero object actually induces all other degenerations by homotopy pullback, that degeneration of 0 is closely linked, but not equivalent, to having zero image in the Grothendieck group.